6.7 Solving Problems Involving Sinusoidal Models.notebook
6.7 Solving Problems Involving Sinusoidal Models.notebook 2015 04 30 April 30, 2015 6.7 Solving Problems Involving Sinusoidal Models Ex. 1 A group of students is tracking a friend, John, who is riding a Ferris wheel. They know that John reaches his maximum height of 11m at 25s and then reaches the minimum height of 1m at 55s. Develop an equation that can be used to determine his height after 78s. 1 6.7 Solving Problems Involving Sinusoidal Models.notebook April 30, 2015 Ex. 2 The top of a flagpole sways back and forth in high winds. The top sways 10 cm to the right (+10 cm) and 10 cm to the left (‐10 cm) of its resting position and moves back and forth 240 times every minute. At t=0, the pole was momentarily at its resting position. Then it started moving to the right. a) Determine the equation of a sinusoidal function that describes the distance the top of the pole is from its resting position in terms of time. b) How does the situation affect the domain and range? c) If the wind speed decreases slightly such that the sway of the top of the pole is reduced by 20%, what is the new equation of the sinusoidal function? Assume that the period remains the same. 2 6.7 Solving Problems Involving Sinusoidal Models.notebook April 30, 2015 Ex. 3 Don Quixote, a fictional character in a Spanish novel, attacked windmills because he thought they were giants. At one point, he got snagged by one of the blades and was hoisted into the air. The graph shows his height above ground in terms of time. a) What is the equation of the axis of the function, and what does it represent in this situation? b) What is the amplitude of the function, and what does it represent in this situation? c) What is the period of the function, and what does it represent in this situation? d) If Don Quixote remains snagged for seven complete cycles, determine the domain and range of the function. e) Determine the equation of the sinusoidal function. f ) If the wind speed decreased, how would that affect the graph of the sinusoidal function? 3 6.7 Solving Problems Involving Sinusoidal Models.notebook April 30, 2015 Ex. 4 Candice is holding onto the end of a spring that is attached to a lead ball. As she moves her hand slightly up and down, the ball moves up and down. With a little concentration, she can repeatedly get the ball to reach a maximum height of 20 cm and a minimum height of 4 cm from the top of a surface. The first maximum height occurs at 0.2 s, and the first minimum height occurs at 0.6 s. a) Determine the equation of the sinusoidal function that represents the height of the lead ball in terms of time. b) Determine the domain and range of the function. c) What is the equation of the axis, and what does it represent in this situation? d) What is the height of the lead ball at 1.3 s? 4 6.7 Solving Problems Involving Sinusoidal Models.notebook April 30, 2015 Ex. 5 A loose nail is attached to one of the paddles on a water wheel. At it's highest point, the nail sits 10.5 feet above the surface of the water. After 12s, the nail reaches it's lowest point 1.5 feet below the surface of the water. a) Determine an equation that can model the height (h) in feet of the nail, t seconds after it is at it's highest point. b) How high is the paddle after 15 seconds? c) Construct a graph of the function. 5 6.7 Solving Problems Involving Sinusoidal Models.notebook April 30, 2015 Pg. 398 #1,3,4,6,9‐10 Tomorrow Review Test Monday PT Ch. 5 and 6 Monday 6
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